Problem: Simplify the following expression: $r = \dfrac{5x^2 + 45x + 100}{x + 5} $
First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $5$ , so we can rewrite the expression: $ r =\dfrac{5(x^2 + 9x + 20)}{x + 5} $ Then we factor the remaining polynomial: $x^2 + {9}x + {20} $ ${5} + {4} = {9}$ ${5} \times {4} = {20}$ $ (x + {5}) (x + {4}) $ This gives us a factored expression: $\dfrac{5(x + {5}) (x + {4})}{x + 5}$ We can divide the numerator and denominator by $(x - 5)$ on condition that $x \neq -5$ Therefore $r = 5(x + 4); x \neq -5$